Abstract
We prove new abstract inequalities for the expectation of the supremum norm of homogeneous Bernoulli polynomials on the unit ball of a Banach space. The development of this type of estimates was stimulated by the classical Kahane–Salem–Zygmund inequality and its recent extensions. We combine ideas from stochastic processes and interpolation theory to control increments of a Rademacher process in an Orlicz space via entropy integrals. To do this we prove general estimates for entropy integrals. We discuss applications to the study of multidimensional Bohr radii and unconditionality in spaces of homogeneous polynomials on Banach spaces. We specialize our results beyond ℓp-spaces and are able to prove variants of Bayart's results in the setting of Orlicz sequence spaces.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
